Hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions

TL;DR

This paper explores the connections between hypergeometric series, their truncated versions, and Gaussian hypergeometric functions by examining higher-dimensional algebraic varieties related to Legendre curves.

Contribution

It introduces new relationships among these hypergeometric objects via the study of higher-dimensional algebraic varieties analogous to Legendre curves.

Findings

Established links between hypergeometric series and algebraic varieties.

Extended classical results to higher-dimensional cases.

Provided new insights into Gaussian hypergeometric functions.

Abstract

In this paper, we investigate the relationships among hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions through some families of `hypergeometric' algebraic varieties that are higher dimensional analogues of Legendre curves.